This invention relates in general to a sensor system and in particular to a sensor system utilizing an improved interferometer.
A sensor is a device that responds to a physical stimulus or field and transmits a resulting response. Different sensors respond to different fields such as pressure, temperature, electric field, magnetic field, electromagnetic radiation or a host of other phenomena. The type of sensor considered here is an analog device so that the larger the field, within certain limits, the larger the resulting response. Thus the sensor can be considered to incorporate as its sensing element a conversion device that converts an evanescent or difficult to quantify field to another easily measured quantity. In this application, the sensing element converts the external field to a modulation of some parameter of an optical system, e.g. a change of the index of refraction in an optical fiber. Various techniques are available that monitor this modulation.
Oftentimes, the magnitude of the field does not need to be measured. Instead, small variations in the field over time will contain a signal of interest. This signal may be the carrier frequency of an infrared communication system that operates against a warm background or it may be a transient magnetic anomaly much smaller than the ambient terrestrial magnetic field. Of course, fields and signals are not limited to the cited examples.
The sensitivity of sensors is often limited by the physical mechanism relied upon in the conversion process of the sensing element. For instance, a method of measuring a magnetic field uses a magnetostrictive material mechanically bonded to an optical fiber to modulate the optical phase length of the fiber. The amount of magnetostriction, i.e. the dilation per unit of magnetic field, is limited in the materials currently available. Nonetheless, such a sensor can be improved by increasing the sensitivity of the optical system to minute changes in its properties and by compensating for various sources of noise.
This application describes techniques and apparatus for increasing the sensitivity of the optical system associated with a sensing element which detects an external field. An adequate sensing element is assumed to exist for whatever field is desired to be detected. For example, Yariv and Winsor describe a magnetostrictive sensor for magnetic fields in Optics Letters, vol 5, 1980, pages 87-89. Other sensing elements exist for other fields.
In one of the simplest fiber optic sensor systems, called a two fiber Mach-Zehnder sensor a source of coherent light excites an optical fiber. The beam is then coupled to a second fiber by means of a directional coupler such that waves of equal amplitude are propagating in both fibers with a fixed phase relation to each other. The sensing element appropriate for the external field is placed on one of the fibers, called the detection fiber. The other fiber, called the reference fiber, is isolated from the field to be measured. At a point at which the wave has passed the sensing element, the detection fiber is coupled to the reference fiber at another directional coupler which causes the wave on one fiber to interfere with the wave on the other fiber. The changes in interference caused by the modulation introduced in the detecting fiber can be used as a measure of the external field.
In mathematical terms, the first directional coupler impresses upon both fibers optical waves of frequency .omega. and of equal complex amplitude E.sub.o. If the physical length of the detection fiber is L.sub.1 and its unmodulated refractive index for the light mode of interest is n, then its phase length is given by: EQU .phi..sub.1 =n.multidot.L.sub.1 .multidot..omega./c (1)
where c is the speed of light. Likewise the reference fiber has a phase length .omega..sub.2. In addition, the sensing element introduces in the detecting fiber a phase modulation .phi.(P) caused by the external field P.
After the waves have been recombined in the second directional coupler, each fiber contains a wave of complex amplitude EQU E.sub.D 1/2E.sub.o (e.sup.i(.phi..sbsp.1 .sup.+.phi.(P) +e.sup.i.multidot..phi..spsb.2) (2)
The behavior of the interferometer is describable in terms of the differential phase length EQU .phi..sub.D =.phi.(P)+.phi..sub.1 -.phi..sub.2 ( 3)
One of the fibers after the second directional coupler connects to an optical detector, the response of which is much slower than .omega., so that the detector's output is proportional to E.sub.D E.sub.D *. Thus the static sensitivity S.sub.S, the ratio of the intensity at the detector to the input intensity, is given for the Mach-Zehnder sensor as EQU S.sub.S,MZ =f.sub.MZ (.phi..sub.D)=1/2(1+cos .phi..sub.D) (4)
This sensitivity is dependent only on the phase difference .phi..sub.D and varies trigonometrically with it. Since in many applications a small signal is impressed on a larger constant field, a more useful sensitivity is the dynamic sensitivity, which is the derivative of S.sub.S with respect to the field impressed phase, i.e. EQU S.sub.D,MZ =dS.sub.S,MZ/d.phi.(P) =-1/2sin .phi..sub.D ( 5)
Thus in operation, a Mach-Zehnder is set to the point of steepest slope of S.sub.S, which is where .phi..sub.D is an odd multiple of .pi./2, in order to obtain the highest S.sub.D.
The usefulness of the Mach-Zehnder interferometer is limited by several factors. First the dynamic sensitivity is not all that great, as will be seen later. Secondly, the two fibers are unintentionally subjected to slightly different environmental noise, such as temperature fluctuations, which cause a differential shift in the phase .phi..sub.1 (Noise.sub.1)-.phi..sub.2 (Noise.sub.2) which is indistinguishable from the phase signal .phi.(P). Thirdly solid state lasers are usually used to provide the coherent light. These lasers however are subject to small random fluctuations in frequency. The impact of these fluctuations can be seen if Eq. (3) is rewritten in terms of Eq. (1) as EQU .phi..sub.D =.phi.(P)+n.multidot.(L.sub.1 -L.sub.2).multidot..omega./c (6)
Unless the lengths of the two fibers, L.sub.1 and L.sub.2, are closely matched in length, then fluctuations in .omega. are indistinguishable from field induced phase shifts .phi.(P). This frequency fluctuation noise is called phase noise.
The last two problems of differing environments and phase noise for a Mach-Zehnder interferometer are greatly alleviated in a single fiber polarimetric interferometric sensor. Rashleigh describes such an acoustic sensor in Optic Letters, vol. 5, 1980, pages 392-394. This polarimetric sensor requires an optical fiber which can support two independent light modes of the same frequency but of mutually perpendicular polarization. This sensor further requires a sensing element which differentially shifts the phase of one of the modes. If the two modes are the x-mode and y-mode, the field produces a differential phase shift EQU .delta..phi.(P)=.phi..sub.x (P)=.phi..sub.y (P) (7)
Rashleigh obtained an interference pattern by placing a Wollaston prism with its axis at 45.degree. to both the x- and y-mode of the fiber. Separate optical detectors measured the intensity of the two beams produced by the Wollaston prism. Electronic circuitry produced a signal proportional to the difference of the intensities. The phase dependence of the difference signal produces a sensitivity very similar to that of Eq. (4). However, phase noise and many sources of environmental noise are eliminated because they are common-mode, i.e. affect both x- and y-modes equally. Nonetheless the sensitivity of the single fiber polarimetric interferometer is somewhat less than that of the Mach-Zehnder because of the use of a differential sensing element.
Sensitivity is greatly increased in a Fabry-Perot interferometer. Petuchowski, Giallorenzi and Sheem describe a fiber-optic Fabry-Perot interferometer in IEEE Journal of Quantum Electronics, vol. QE-17, 1981, pages 2168-2170. The ends of an optical fiber are made highly but not completely reflecting with reflection coefficients of r.sub.1 and r.sub.2. A coherent light source launches a light wave through one end of the fiber. A sensing element modulates the phase of the wave. An optical detector measures the intensity of the light transmitted through the other end of the fiber. The light wave interferes with itself as it reflects between the two ends. The static sensitivity is the transmission coefficient of the interferometer given by EQU S.sub.S,FP =T.sub.max .multidot.f.sub.FP (.phi.) (8)
where EQU T.sub.max =(1-r.sub.1).sup.2 .multidot.(1-r.sub.2.sup.2)/(1-a.multidot.r.sub.1 .multidot.r.sub.2) (8)
and the attenuation per pass is (1-a). The phase dependent factor is given by EQU f.sub.FP (.phi.)=(1+.rho..multidot.sin.sup.2 .phi.).sup.-1 ( 10)
where .rho. is defined as EQU .rho.=4.multidot.a.multidot.r.sub.1 .multidot.r.sub.2 /(1-a.multidot.r.sub.1 .multidot.r.sub.2).sup.2 ( 11)
Inspection of Equations (10) and (11) shows that for relatively high reflection coeffiecients, the static sensitivity is strongly peaked near the resonances where the reflecting light positively interferes and results in significant transmission. As a result the dynamic sensitivity can be very large if the interferometer is operated on the side of the peak of Equation (10).
Thus a Fabry-Perot interferometric sensor can exhibit much higher sensitivity than a Mach-Zehnder system. However the high sensitivity applies to noise as well as signal. As described thus far there are no noise cancelling properties inherent in the Fabry-Perot interferometer so that noise is even more troublesome than for the Mach-Zehnder interferometer.